10. 1) Запишите формулу производной для функции у=e", у=а*. 2) Найдите производную функции: a) u(x)=5-24-3x; B) g(x)=e-3x; 6) u(x)=3.57-1 2x r) f(x)=(+)

Формулы производных:

• (eˣ)' = eˣ
• (aˣ)' = aˣ ⋅ ln(a)

Найдите производную функции:

1. v(x) = 5 - 2e⁻³ˣ:

   v'(x) = -2 ⋅ e⁻³ˣ ⋅ (-3) = 6e⁻³ˣ

2. u(x) = 3 ⋅ 5⁷ˣ⁻¹:

   u'(x) = 3 ⋅ 5⁷ˣ⁻¹ ⋅ ln(5) ⋅ 7 = 21ln(5) ⋅ 5⁷ˣ⁻¹

3. g(x) = e⁻³ˣ:

   g'(x) = e⁻³ˣ ⋅ (-3) = -3e⁻³ˣ

4. f(x) = (⅓)²ˣ:

   f'(x) = (⅓)²ˣ ⋅ ln(⅓) ⋅ 2 = 2(⅓)²ˣ ⋅ ln(⅓)